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For example my hero currently does a 15% lifesteal from it's basic attack of 50. When it trigger a critical strike doubling my damage to 100, does my lifesteal also doubles the amount?

Is it the same for double damage?

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    Is this for Dota, or Dota 2? They are two games from entirely different groups, so only one tag is needed.
    – Niro
    Oct 22, 2012 at 13:12
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    The lifesteal mechanics are the same in both games. I don't know how you can say they're from entirely different groups since gameplay wise they're virtually identical.
    – Decency
    Oct 22, 2012 at 23:51
  • Both game engines have their limitations, mainly the WC3 version. There are some minor differences between the games.
    – jzacharia
    Nov 9, 2012 at 18:57

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Lifesteal is calculated after all damage enhancements and reductions have taken place.

So that means that any Skill, item, enhancement, aura or effect which increases your base damage will affect lifesteal, because it is applied AFTER all those have taken place. Except in cases where a Conditional Modifier or Ability Modifier takes priority (if lifesteal is from an item) see wiki

Examples

Critical Strike Lifesteal is calculated after Critical Strikes which means that it will increase the amount of life you steal.

Double Damage - +100% damage on your base damage and any attribute increasing effects Also increases the amount of life you steal

Dota 2 Wiki - Lifesteal

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    Worth noting is that some passive abilities like Anti-Mage's Mana Break also benefit from lifesteal. I'm not sure which other abilities would count.
    – Decency
    Oct 22, 2012 at 23:53
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Double damage rune just double the base damage + attributes of your hero, and it comes before all other effects/orbs. Lifesteal instead is calculated after all other effects and also after all damage reductions, therefore we can affirm that lifesteal will benefits from a double damage rune.

Regarding Critical Strickes, as described also on Dota 2 Wiki, they also increase the total amount of life steal per hit.

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Short answer is yes.

Practical answer; if you have lifesteal coming from a non orb source (aura, innate ex: lifestealer passive) it is almost always better mathematically to buy Desolator before critical strike against most targets with most armor values you are likely to see in game.

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